Ben Davison
Title: Critical stable envelopes and BPS cohomology
Abstract:
In this talk I will introduce the nonabelian stable envelope, a construction of Aganagic and Okounkov which, cast in terms of cohomology, can be viewed as a canonical section of the morphism from tautological classes to the cohomology of Nakajima quiver varieties. This can be recast as a canonical right inverse to the morphism in Borel-Moore homology induced by the inclusion of the stack of semistable objects inside the stack of all representations of a certain category.
In recent joint work with Tommaso Botta, we prove that the nonabelian stable envelope may be identified with the inclusion of BPS cohomology (which I'll define). This turns out to be the key result along the way to our recent proof that certain BPS Lie algebras may be identified with the Maulik-Okounkov Lie algebras appearing in their construction of Yangians out of stable envelopes, which implies Okounkov's conjecture identifying the graded dimensions of their Lie algebras with coefficients of Kac polynomials.
Soheyla Feyzbakhsh
Title: Relations of Kuznetsov components of a Gushel-Mukai variety and its hyperplane sections
Abstract:
Let X be a very general Gushel–Mukai variety of dimension n>3, and let Y be a smooth hyperplane section. There are natural pull-back and push-forward functors between the semi-orthogonal components (known as the Kuznetsov components) of the derived categories of X and Y. In this talk, I will show that the Bridgeland stability of objects is preserved under both of these functors and discuss some applications of this result. Joint work with Henfei Guo, Zhiyu Liu and Shizhuo Zhang.
Kohei Kikuta
Title: Geometrical finiteness for automorphism groups via cone conjecture
Abstract:
Geometrical finiteness is one of the central notions in the study of Kleinian groups. In this talk, we explain the geometrical finiteness for the natural isometric actions of (birational) automorphism groups on the hyperbolic spaces for K3 surfaces, Enriques surfaces, Coble surfaces, and irreducible symplectic varieties. Then the cone conjecture is a key to the proof. If time permits, some applications for K3 surfaces will be discussed.
Naoki Koseki
Title: Gopakumar-Vafa invariants of local curves
Abstract:
In 1990s, two physisists, Gopakumar and Vafa, proposed an ideal way to count curves in a Calabi-Yau threefold, that is conjecturally equivalent to other curve counting theories such as Gromov-Witten theory. It is very recent that Maulik and Toda gave a mathematically rigorous definition of GV invariants. In this talk, I will review a recent progress on GV theory, including chi-independence for GV invariants on local curves and GW/GV equivalence for some smooth curves with generic normal bundles. This is based on a joint work with T. Kinjo and another work with B. Davison.